Pathway XIV

μMeasure theory and Lᵖ

Length of wild sets, then spaces of functions with integrable p-th power.

1. 01Lebesgue measureCover a set by intervals, sum the lengths, take the infimum. That is outer measure.4 min
2. 02Lᵖ spaces||f||ₚ = (∫ |f|ᵖ)^{1/p}. As p grows, the unit ball of Lᵖ in ℝ² morphs from diamond to circle to square.4 min